Place A Rack In The Center Of The Oven, And Preheat The Oven To 375°F.
Rub The Soft Butter On The Bottom And Sides Of An 8″ Springform Pan Or Tall Metal Baking Pan With Removable Bottom.
Dust With The Cocoa, And Set The Pan Aside.
Place The Chocolate And Butter In A Heavy Saucepan Over Low Heat, And Stir Until The Chocolate Melts, 2 Minutes.
Turn Off The Heat And Set The Chocolate-Butter Mixture Aside.
Separate The Eggs, Placing The Yolks In A Large Mixing Bowl And The Whites In A Separate Large Mixing Bowl.
Set The Whites Aside.
Beat The Egg Yolks With An Electric Mixer On Medium-High Speed, Gradually Adding ¾ Cup Of The Sugar As You Beat.
Beat Until They Are Pale Yellow And The Consistency Of Mayonnaise, 1 To 2 Minutes.
Turn Off The Mixer And Pour The Chocolate Mixture Into The Yolks.
Beat On Low Until Just Combined, 30 Seconds.
Add The Rum And Vanilla, And Beat Again On Low Until Just Combined, 10 Seconds.
Set Aside.
With Clean Beaters, Beat The Egg Whites On High Speed Until Soft Peaks Form, 1 To 2 Minutes.
Gradually Beat In The Remaining ¼ Cup Sugar, And Beat Until Stiff Peaks Form, About 1 Minute Longer.
Turn Off The Mixer, And Fold The Whites Into The Chocolate Mixture With A Rubber Spatula Until The Whites Are Well Combined.
Pour The Batter Into The Prepared Pan, And Place The Pan In The Oven.
Bake The Cake For 15 Minutes, Then Reduce The Temperature To 350°F, Leaving The Cake In The Oven.
Bake The Cake For Another 15 Minutes, Then Reduce The Temperature To 250°F.
Bake The Cake Until The Cake Smells Very Chocolatey, The Top Has A Nice Firm Crust, And The Cake Jiggles A Bit When The Top Is Touched, 20 To 25 Minutes.
Turn Off The Oven, But Leave The Cake In The Oven.
Prop The Oven Door Open 2″ With Kitchen Towels, And Let The Cake Sit In The Turned-Off Oven For 25 Minutes.
Remove The Cake From The Oven, And Let It Cool For 20 To 30 Minutes In The Pan On The Kitchen Counter.
The Cake Will Fall As It Cools.
Run A Knife Around The Edge Of The Pan, And Remove The Sides Or Bottom Of The Pan.
Place The Cake On A Serving Plate, Sift Confectioners’ Sugar Over The Top, And Slice While Warm.
Serve With The Ice Cream And/Or Berries.
Or, For Easier Slicing, Leave The Cake In The Pan And Chill, Covered, At Least 2 Hours, Then Slice And Serve.
